Seismic imaging faces challenges due to the presence of several uncertainty sources. Uncertainties exist in data measurements, source positioning, and subsurface geophysical properties. Reverse time migration (RTM) is a high-resolution depth migration approach useful for extracting information such as reservoir localization and boundaries. RTM, however, is time-consuming and data-intensive as it requires computing twice the wave equation to generate and store an imaging condition. RTM, when embedded in an uncertainty quantification algorithm (like the Monte Carlo method), shows a many-fold increase in its computational complexity due to the high input-output dimensionality. In this work, we propose an encoder-decoder deep learning surrogate model for RTM under uncertainty. Inputs are an ensemble of velocity fields, expressing the uncertainty, and outputs the seismic images. We show by numerical experimentation that the surrogate model can reproduce the seismic images accurately, and, more importantly, the uncertainty propagation from the input velocity fields to the image ensemble.

由于存在多个不确定性源，地震成像面临挑战。在数据测量，震源定位和地下地球物理属性方面存在不确定性。逆时偏移（RTM）是一种高分辨率的深度偏移方法，可用于提取诸如储层定位和边界之类的信息。但是，RTM既耗时又需要大量数据，因为它需要计算两次波动方程才能生成并存储成像条件。RTM嵌入不确定性量化算法（如蒙特卡洛方法）后，由于高输入-输出维数，其计算复杂性增加了许多倍。在这项工作中，我们提出了不确定性下RTM的编解码器深度学习替代模型。输入是速度场的整体，表示不确定性，并输出地震图像。通过数值实验表明，替代模型可以准确地再现地震图像，更重要的是，不确定性从输入速度场传播到图像集合。